the production function is f(x₁, x₂)= x^1/2₁x^1/2₂.If the price of factor 1 is $10 and the price of factor 2 is $20, in what proportions should the firm use factors 1 and 2 if it wants to maximize profits? A)We can't tell without knowing the price of output. B)x₁ =2x₂. C)x₁ = 0.50x₂. D)x₁ = x₂. E)x₁ = 20x₂.

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Quizplus · Accepted Answer

The profit-maximizing condition is that the marginal rate of technical substitution (MRTS) equals the ratio of factor prices. The MRTS is defined as the change in the quantity of factor 1 that is required to keep output constant when the quantity of factor 2 is increased by one unit. In this case, the MRTS is equal to:MRTS = (dF/dx1)/(dF/dx2) = (1/2)x1^(-1/2)x2^(1/2)/(1/2)x1^(1/2)x2^(-1/2) = x1/x2The ratio of factor prices is equal to:w1/w2 = 10/20 = 1/2Therefore, the profit-maximizing condition is:MRTS = w1/w2x1/x2 = 1/2x1 = 2x2

The Production Function Is F(x1, X2)= X1/21x1/22

The Production Function Is F(x₁, X₂)= X^1/2₁x^1/2₂